Orthogonal Projections

7.1  Orthogonal Projections
Definition of Plane

The flat surface of an object.

Types of planes:
  • Horizontal plane
  • Vertical plane
  • Inclined plane
Definition of Normal to a Plane

A straight line that is perpendicular or that forms a right angle to any line on the plane.

Definition of Orthogonal Projections

Images formed on a plane when the projected line from an object is perpendicular to the plane.



The diagram above shows the projection of an object on a vertical plane.

The resulting projection is an orthogonal projection because the line projected from an object to the plane is normal.

Steps to draw an orthogonal projection:
  1. Identify the type of plane and the direction in which the object should be projected.
  2. Draw normal lines from all vertices of the object to the plane. Make sure all the normal lines are straight and upright so that the length of projected sides and the length of sides of the object are the same.
  3. Connect the points of intersection of the normal to the plane to draw the shape of orthogonal projection.
  4. Redraw the orthogonal projection with actual measurements. Label all vertices and side lengths.

The following diagram shows a cylindrical object on a horizontal plane.


Given that the diameter of the cylinder is \(4 \text{ cm}\) and its height is \(6 \text{ cm}\).


a) Draw the orthogonal projection of the cylindrical object on a horizontal plane as viewed from \(Z\).

Viewing direction               Orthogonal projection           


b) Draw the orthogonal projection of the cylindrical object on a vertical plane as viewed from \(Y\).

Viewing direction Orthogonal projection

  • The length of sides and size of angles of the orthogonal projections of an object can remain unchanged or vary according to the viewing direction.